Preheat the oven to 350°F. Line two baking sheets with parchment paper or silicone baking mats and set them aside.
Using a stand mixer or hand mixer and large bowl, cream together butter, shortening, and sugar until light and fluffy (about 5 minutes).
Beat in eggs, vanilla, and instant pudding mix.
In another bowl, whisk together flour, baking powder, and salt. Gradually add to the butter mixture, a little at a time, mixing between additions.
Using a cookie scoop or Tablespoon, scoop the dough out, roll it into balls, and place it onto the lined cookie sheets with each cookie about 2 inches apart.
Bake for 12-15 minutes or until set and lightly golden brown around the edges. Allow the cookies to cool on the cookie sheet for 5 minutes, then transfer to a cooling rack to cool fully.
To make the frosting, beat butter until light and fluffy, about 3 minutes. Add powdered sugar and heavy cream a little at a time, alternating and mixing between additions. Add vanilla and salt; mix until well incorporated.
Separate frosting into one bowl per color and stir in a few drops of gel food coloring. Add additional drops if needed, until the desired color is reached.
Frost cooled cookies and immediately top with sprinkles.
Allow frosting to set before storing in an airtight container until serving.
Notes
Your soft Christmas frosted cookies will keep for up to 4 days in an airtight container at room temperature or up to 1 week in the fridge.I would recommend storing the cookies in a single layer or with parchment paper between layers so that the frosting doesn’t stick to the other cookies.The cookie dough can be made ahead and stored in the refrigerator until ready to bake, up to 3 days. Or store the cookie dough in the freezer for up to 3 months.